Obviously, \(\bar{w}_{a_s^{*}}\lnot \equiv 0\)  by (REF ).
Moreover, it follows from (REF ) that \(\bar{w}_{a_s^{*}}\)  satisfies the following Pohozaev type identity (see e.g., [1]}),
\(\int _{\mathbb {R}^{N}}|\bar{w}_{a_s^{*}}|^{\frac{4s}{N}+2}dx= \frac{N+2s}{Na_s^{*}m(\bar{x}_{0})}\int _{\mathbb {R}^{N}}|(-\Delta )^{\frac{s}{2}}\bar{w}_{a_s^{*}}|^{2}dx.\) 
